Nonlinear Dynamics

, Volume 86, Issue 2, pp 1293–1318 | Cite as

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

  • O. ThomasEmail author
  • A. Sénéchal
  • J.-F. Deü
Original Paper


This work addresses the large amplitude nonlinear vibratory behavior of a rotating cantilever beam, with applications to turbomachinery and turbopropeller blades. The aim of this work is twofold. Firstly, we investigate the effect of rotation speed on the beam nonlinear vibrations and especially on the hardening/softening behavior of its resonances and the appearance of jump phenomena at large amplitude. Secondly, we compare three models to simulate the vibrations. The first two are based on analytical models of the beam, one of them being original. Those two models are discretized on appropriate mode basis and solve by a numerical following path method. The last one is based on a finite-element discretization and integrated in time. The accuracy and the validity range of each model are exhibited and analyzed.


Large rotation Nonlinear von Karman Biot strain Inextensible Continuation method Asymptotic numerical method Modal expansion 



The French company Safran Snecma and the French Ministry of Research are thanked for the financial support of this study, through the PhD grant of the second author. Émmanuel Cottanceau is also warmly thanked for the careful reading of the finite-element model details section.


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Authors and Affiliations

  1. 1.LSIS UMR CNRS 7296Arts et Métiers ParisTechLilleFrance
  2. 2.Structural Mechanics and Coupled Systems Laboratory, CnamParisFrance
  3. 3.Airbus Defence and SpaceLes MureauxFrance

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